Question

The sum of two numbers is 63. One number is five less than three times the other. What's the answer?

Answer 1

`17 and 46`

Explanation:

Turn each of the phrases into math equations, and then solve. Since there are two numbers, I will call one `x` and the other `y`.

`stackrel(x + y)overbrace"The sum of two numbers"stackrel(=)overbrace"is"stackrel(63)overbrace"63"`

`stackrel(x)overbrace"one number"stackrel(=)overbrace"is"stackrel(3y - 5)overbrace"five less than three times the other"`

`x +y = 63`

`x = 3y - 5`

Substitute the second equation into the first one:

`x + y = 63`

`(3y - 5) + y = 63`

`3y - 5 + y = 63`

`4y - 5 = 63`

`4y = 68`

`y = 17`

Now substitute the value for `y` into one of the equations and solve:

`x = 3y - 5`

`x = 3(17) -5`

`x = 51 - 5`

`x = 46`

So the two numbers are `17` and `46`.